New Instability of a Thin Vortex Ring in an Ideal Fluid

Abstract—The problem of stability of steady-state thin vortex ring flow in an ideal fluid is studied in the linear approximation. The case of the isochronous vortex ring in which the liquid-particle rotation periods are identical is considered. In such a flow there are no perturbations of the continuous spectrum. This makes considerably easier to solve this complex problem. The instability of longwave oscillations related to the interaction between the perturbations with energy of different signs, namely, the oscillations with positive and negative energy, is revealed.